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[matrix] Annotation of /pkg/Matrix/R/diagMatrix.R
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Annotation of /pkg/Matrix/R/diagMatrix.R

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1 : maechler 1617 #### All methods for "diagonalMatrix" and its subclasses,
2 :     #### currently "ddiMatrix", "ldiMatrix"
3 :    
4 : maechler 1109 ## Purpose: Constructor of diagonal matrices -- ~= diag() ,
5 :     ## but *not* diag() extractor!
6 :     Diagonal <- function(n, x = NULL)
7 :     {
8 : mmaechler 2820 ## Allow Diagonal(4), Diagonal(x=1:5), and Diagonal(4, TRUE)
9 : maechler 1109 if(missing(n))
10 : maechler 1575 n <- length(x)
11 : maechler 1109 else {
12 : maechler 1575 stopifnot(length(n) == 1, n == as.integer(n), n >= 0)
13 :     n <- as.integer(n)
14 : maechler 1109 }
15 :    
16 : maechler 1654 if(missing(x)) ## unit diagonal matrix
17 : maechler 1575 new("ddiMatrix", Dim = c(n,n), diag = "U")
18 : maechler 1109 else {
19 : maechler 2128 lx <- length(x)
20 : mmaechler 2820 lx.1 <- lx == 1L
21 :     stopifnot(lx.1 || lx == n) # but keep 'x' short for now
22 : maechler 1575 if(is.logical(x))
23 :     cl <- "ldiMatrix"
24 :     else if(is.numeric(x)) {
25 :     cl <- "ddiMatrix"
26 :     x <- as.numeric(x)
27 :     }
28 :     else if(is.complex(x)) {
29 :     cl <- "zdiMatrix" # will not yet work
30 :     } else stop("'x' has invalid data type")
31 : mmaechler 2820 if(lx.1 && !is.na(x) && x == 1) # cheap check for uni-diagonal..
32 :     new(cl, Dim = c(n,n), diag = "U")
33 :     else
34 :     new(cl, Dim = c(n,n), diag = "N",
35 :     x = if(lx.1) rep.int(x,n) else x)
36 : maechler 1109 }
37 :     }
38 :    
39 : mmaechler 2840 .sparseDiagonal <- function(n, x = 1, uplo = "U",
40 : mmaechler 2508 shape = if(missing(cols)) "t" else "g",
41 : mmaechler 2840 unitri, kind,
42 :     cols = if(n) 0:(n - 1L) else integer(0))
43 : mmaechler 2508 {
44 : maechler 2144 stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0)
45 : mmaechler 2840 if(!(mcols <- missing(cols)))
46 : mmaechler 2508 stopifnot(0 <= (cols <- as.integer(cols)), cols < n)
47 :     m <- length(cols)
48 :     if(missing(kind))
49 :     kind <-
50 :     if(is.double(x)) "d"
51 :     else if(is.logical(x)) "l"
52 :     else { ## for now
53 :     storage.mode(x) <- "double"
54 :     "d"
55 :     }
56 :     else stopifnot(any(kind == c("d","l","n")))
57 : mmaechler 2226 stopifnot(is.character(shape), nchar(shape) == 1,
58 :     any(shape == c("t","s","g"))) # triangular / symmetric / general
59 : mmaechler 2840 if((missing(unitri) || unitri) && shape == "t" &&
60 :     (mcols || cols == 0:(n-1L)) &&
61 :     ((any(kind == c("l", "n")) && allTrue(x)) ||
62 :     ( kind == "d" && allTrue(x == 1)))) { ## uni-triangular
63 :     new(paste0(kind,"tCMatrix"), Dim = c(n,n),
64 :     uplo = uplo, diag = "U", p = rep.int(0L, n+1L))
65 :     }
66 :     else if(kind == "n") {
67 : mmaechler 2508 if(shape == "g")
68 :     new("ngCMatrix", Dim = c(n,m), i = cols, p = 0:m)
69 :     else new(paste0("n", shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
70 :     i = cols, p = 0:m)
71 :     }
72 : mmaechler 2840 else { ## kind != "n" -- have x slot :
73 :     if((lx <- length(x)) == 1) x <- rep.int(x, m)
74 :     else if(lx != m) stop("length(x) must be either 1 or #{cols}")
75 :     if(shape == "g")
76 :     new(paste0(kind, "gCMatrix"), Dim = c(n,m),
77 :     x = x, i = cols, p = 0:m)
78 :     else new(paste0(kind, shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
79 :     x = x, i = cols, p = 0:m)
80 :     }
81 : maechler 2144 }
82 :    
83 : mmaechler 2226 ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I()
84 :     .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
85 :     .sparseDiagonal(n, x, uplo, shape = "s")
86 :    
87 : mmaechler 2608 # instead of diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case:
88 : mmaechler 2840 .trDiagonal <- function(n, x = 1, uplo = "U", unitri=TRUE)
89 :     .sparseDiagonal(n, x, uplo, shape = "t", unitri=unitri)
90 : mmaechler 2226
91 :    
92 : mmaechler 2764 ## This is modified from a post of Bert Gunter to R-help on 1 Sep 2005.
93 :     ## Bert's code built on a post by Andy Liaw who most probably was influenced
94 :     ## by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
95 :     ## who posted his bdiag() function written in December 1995.
96 : mmaechler 2209 if(FALSE)##--- no longer used:
97 : mmaechler 2206 .bdiag <- function(lst) {
98 : mmaechler 2764 ## block-diagonal matrix [a dgTMatrix] from list of matrices
99 : mmaechler 2206 stopifnot(is.list(lst), length(lst) >= 1)
100 : mmaechler 2813 dims <- vapply(lst, dim, 1L, USE.NAMES=FALSE)
101 : maechler 1617 ## make sure we had all matrices:
102 :     if(!(is.matrix(dims) && nrow(dims) == 2))
103 :     stop("some arguments are not matrices")
104 : maechler 1845 csdim <- rbind(rep.int(0L, 2),
105 : mmaechler 2206 apply(dims, 1, cumsum))
106 :     r <- new("dgTMatrix")
107 :     r@Dim <- as.integer(csdim[nrow(csdim),])
108 : maechler 1617 add1 <- matrix(1:0, 2,2)
109 : mmaechler 2206 for(i in seq_along(lst)) {
110 : maechler 1617 indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
111 :     if(is.null(dim(indx))) ## non-square matrix
112 : mmaechler 2206 r[indx[[1]],indx[[2]]] <- lst[[i]]
113 : maechler 1617 else ## square matrix
114 : mmaechler 2206 r[indx[,1], indx[,2]] <- lst[[i]]
115 : maechler 1617 }
116 : mmaechler 2206 r
117 : maechler 1617 }
118 : mmaechler 2209 ## expand(<mer>) needed something like bdiag() for lower-triangular
119 :     ## (Tsparse) Matrices; hence Doug Bates provided a much more efficient
120 :     ## implementation for those; now extended and generalized:
121 : mmaechler 2206 .bdiag <- function(lst) {
122 : mmaechler 2209 ## block-diagonal matrix [a dgTMatrix] from list of matrices
123 : mmaechler 2206 stopifnot(is.list(lst), (nl <- length(lst)) >= 1)
124 : maechler 1617
125 : mmaechler 2206 Tlst <- lapply(lapply(lst, Matrix:::as_Csp2), # includes "diagU2N"
126 : mmaechler 2209 as, "TsparseMatrix")
127 : mmaechler 2206 if(nl == 1) return(Tlst[[1]])
128 :     ## else
129 : mmaechler 2813 i_off <- c(0L, cumsum(vapply(Tlst, nrow, 1L)))
130 :     j_off <- c(0L, cumsum(vapply(Tlst, ncol, 1L)))
131 : mmaechler 2209
132 : mmaechler 2813 clss <- vapply(Tlst, class, "")
133 : mmaechler 2741 typ <- substr(clss, 2, 2)
134 :     knd <- substr(clss, 1, 1)
135 :     sym <- typ == "s" # symmetric ones
136 :     tri <- typ == "t" # triangular ones
137 :     use.n <- any(is.n <- knd == "n")
138 :     if(use.n && !(use.n <- all(is.n))) {
139 : mmaechler 2209 Tlst[is.n] <- lapply(Tlst[is.n], as, "lMatrix")
140 : mmaechler 2741 knd [is.n] <- "l"
141 :     }
142 :     use.l <- !use.n && all(knd == "l")
143 : mmaechler 2209 if(all(sym)) { ## result should be *symmetric*
144 : mmaechler 2813 uplos <- vapply(Tlst, slot, ".", "uplo") ## either "U" or "L"
145 : mmaechler 2209 tLU <- table(uplos)# of length 1 or 2 ..
146 :     if(length(tLU) == 1) { ## all "U" or all "L"
147 :     useU <- uplos[1] == "U"
148 :     } else { ## length(tLU) == 2, counting "L" and "U"
149 :     useU <- diff(tLU) >= 0
150 :     if(useU && (hasL <- tLU[1] > 0))
151 :     Tlst[hasL] <- lapply(Tlst[hasL], t)
152 :     else if(!useU && (hasU <- tLU[2] > 0))
153 :     Tlst[hasU] <- lapply(Tlst[hasU], t)
154 :     }
155 :     if(use.n) { ## return nsparseMatrix :
156 :     r <- new("nsTMatrix")
157 :     } else {
158 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "sTMatrix"))
159 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
160 :     }
161 :     r@uplo <- if(useU) "U" else "L"
162 :     }
163 : mmaechler 2813 else if(all(tri) && { ULs <- vapply(Tlst, slot, ".", "uplo")## "U" or "L"
164 : mmaechler 2209 all(ULs[1L] == ULs[-1L]) } ## all upper or all lower
165 :     ){ ## *triangular* result
166 :    
167 :     if(use.n) { ## return nsparseMatrix :
168 :     r <- new("ntTMatrix")
169 :     } else {
170 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "tTMatrix"))
171 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
172 :     }
173 :     r@uplo <- ULs[1L]
174 :     }
175 :     else {
176 :     if(any(sym))
177 :     Tlst[sym] <- lapply(Tlst[sym], as, "generalMatrix")
178 :     if(use.n) { ## return nsparseMatrix :
179 :     r <- new("ngTMatrix")
180 :     } else {
181 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "gTMatrix"))
182 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
183 :     }
184 :     }
185 :     r@Dim <- c(i_off[nl+1], j_off[nl + 1])
186 :     r@i <- unlist(lapply(1:nl, function(k) Tlst[[k]]@i + i_off[k]))
187 :     r@j <- unlist(lapply(1:nl, function(k) Tlst[[k]]@j + j_off[k]))
188 :     r
189 : mmaechler 2206 }
190 :    
191 :     bdiag <- function(...) {
192 :     if((nA <- nargs()) == 0) return(new("dgCMatrix"))
193 :     if(nA == 1 && !is.list(...))
194 :     return(as(..., "CsparseMatrix"))
195 :     alis <- if(nA == 1 && is.list(..1)) ..1 else list(...)
196 :     if(length(alis) == 1)
197 :     return(as(alis[[1]], "CsparseMatrix"))
198 :    
199 :     ## else : two or more arguments
200 :     as(.bdiag(alis), "CsparseMatrix")
201 :     }
202 :    
203 :    
204 : maechler 2136 .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
205 :     ## to triangular Tsparse
206 : maechler 1845 i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
207 : mmaechler 2778 new(paste0(kind, "tTMatrix"),
208 : maechler 1654 diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
209 : maechler 2128 uplo = uplo,
210 : maechler 1654 x = from@x, # <- ok for diag = "U" and "N" (!)
211 :     i = i, j = i)
212 :     }
213 : maechler 1109
214 : maechler 2136 .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
215 :     ## to symmetric Tsparse
216 : maechler 2128 n <- from@Dim[1]
217 :     i <- seq_len(n) - 1L
218 : mmaechler 2778 new(paste0(kind, "sTMatrix"),
219 : maechler 1845 Dim = from@Dim, Dimnames = from@Dimnames,
220 : maechler 2128 i = i, j = i, uplo = uplo,
221 :     x = if(from@diag == "N") from@x else ## "U"-diag
222 :     rep.int(switch(kind,
223 :     "d" = 1.,
224 :     "l" =,
225 :     "n" = TRUE,
226 :     ## otherwise
227 :     stop("'", kind,"' kind not yet implemented")), n))
228 : maechler 1845 }
229 :    
230 : maechler 2128 ## diagonal -> triangular, upper / lower depending on "partner":
231 : maechler 2144 diag2tT.u <- function(d, x, kind = .M.kind(d))
232 :     .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
233 : maechler 2128
234 : mmaechler 2175 ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
235 :     diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
236 :     clx <- getClassDef(class(x))
237 :     if(extends(clx, "symmetricMatrix"))
238 :     .diag2sT(d, uplo = x@uplo, kind)
239 :     else
240 :     .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
241 :     }
242 : maechler 2136
243 : mmaechler 2814 ## FIXME: should not be needed {when ddi* is dsparse* etc}:
244 :     setMethod("is.finite", signature(x = "diagonalMatrix"),
245 :     function(x) is.finite(.diag2tT(x)))
246 :     setMethod("is.infinite", signature(x = "diagonalMatrix"),
247 :     function(x) is.infinite(.diag2tT(x)))
248 : mmaechler 2175
249 : maechler 2136 ## In order to evade method dispatch ambiguity warnings,
250 :     ## and because we can save a .M.kind() call, we use this explicit
251 :     ## "hack" instead of signature x = "diagonalMatrix" :
252 :     ##
253 :     ## ddi*:
254 :     diag2tT <- function(from) .diag2tT(from, "U", "d")
255 :     setAs("ddiMatrix", "triangularMatrix", diag2tT)
256 : mmaechler 2239 ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", diag2tT)
257 : maechler 1805 ## needed too (otherwise <dense> -> Tsparse is taken):
258 : maechler 2136 setAs("ddiMatrix", "TsparseMatrix", diag2tT)
259 : mmaechler 2482 setAs("ddiMatrix", "dsparseMatrix", diag2tT)
260 : maechler 2136 setAs("ddiMatrix", "CsparseMatrix",
261 :     function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
262 :     setAs("ddiMatrix", "symmetricMatrix",
263 :     function(from) .diag2sT(from, "U", "d"))
264 :     ##
265 :     ## ldi*:
266 :     diag2tT <- function(from) .diag2tT(from, "U", "l")
267 :     setAs("ldiMatrix", "triangularMatrix", diag2tT)
268 : mmaechler 2239 ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", diag2tT)
269 : maechler 2136 ## needed too (otherwise <dense> -> Tsparse is taken):
270 :     setAs("ldiMatrix", "TsparseMatrix", diag2tT)
271 : mmaechler 2482 setAs("ldiMatrix", "lsparseMatrix", diag2tT)
272 : maechler 2136 setAs("ldiMatrix", "CsparseMatrix",
273 :     function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
274 :     setAs("ldiMatrix", "symmetricMatrix",
275 :     function(from) .diag2sT(from, "U", "l"))
276 : maechler 1654
277 : maechler 1845
278 : maechler 2128 setAs("diagonalMatrix", "nMatrix",
279 :     function(from) {
280 :     n <- from@Dim[1]
281 :     i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
282 :     new("ntTMatrix", i = i, j = i, diag = from@diag,
283 :     Dim = from@Dim, Dimnames = from@Dimnames)
284 :     })
285 :    
286 : mmaechler 2237 setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))
287 : maechler 2128
288 : mmaechler 2175 ## Cheap fast substitute for diag() which *does* preserve the mode of x :
289 :     mkDiag <- function(x, n) {
290 :     y <- matrix(as0(mod=mode(x)), n,n)
291 : mmaechler 2820 if (n > 0) y[1L + 0:(n - 1L) * (n + 1)] <- x
292 : mmaechler 2175 y
293 :     }
294 :    
295 : maechler 1109 setAs("diagonalMatrix", "matrix",
296 :     function(from) {
297 : mmaechler 2175 ## want "ldiMatrix" -> <logical> "matrix" :
298 :     mkDiag(if(from@diag == "U") as1(from@x) else from@x,
299 :     n = from@Dim[1])
300 : maechler 1109 })
301 :    
302 : maechler 2098 setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
303 :     function(x, mode) {
304 :     n <- x@Dim[1]
305 : mmaechler 2175 mod.x <- mode(x@x)
306 :     r <- vector(mod.x, length = n^2)
307 : maechler 2098 if(n)
308 : mmaechler 2820 r[1 + 0:(n - 1L) * (n + 1)] <-
309 : mmaechler 2175 if(x@diag == "U") as1(mod=mod.x) else x@x
310 : maechler 2098 r
311 :     })
312 :    
313 : maechler 1654 setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
314 : maechler 2128 function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
315 : maechler 1174
316 : mmaechler 2268 setAs("diagonalMatrix", "denseMatrix",
317 :     function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))
318 :    
319 : mmaechler 2185 .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
320 : maechler 1655
321 :     .diag.2N <- function(m) {
322 :     if(m@diag == "U") m@diag <- "N"
323 :     m
324 :     }
325 :    
326 : maechler 1174 setAs("ddiMatrix", "dgeMatrix",
327 : mmaechler 2183 function(from) .Call(dup_mMatrix_as_dgeMatrix, from))
328 :     setAs("ddiMatrix", "ddenseMatrix",
329 :     function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
330 :     setAs("ldiMatrix", "ldenseMatrix",
331 :     function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
332 : maechler 1174
333 : mmaechler 2183
334 : maechler 1109 setAs("matrix", "diagonalMatrix",
335 :     function(from) {
336 : maechler 1295 d <- dim(from)
337 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
338 :     if(any(from[row(from) != col(from)] != 0))
339 : mmaechler 2341 stop("matrix with non-zero off-diagonals cannot be coerced to diagonalMatrix")
340 : maechler 1295 x <- diag(from)
341 :     if(is.logical(x)) {
342 :     cl <- "ldiMatrix"
343 : mmaechler 2341 uni <- allTrue(x) ## uni := {is it unit-diagonal ?}
344 : maechler 1295 } else {
345 :     cl <- "ddiMatrix"
346 : mmaechler 2341 uni <- allTrue(x == 1)
347 : maechler 1295 storage.mode(x) <- "double"
348 : maechler 1575 } ## TODO: complex
349 : maechler 1295 new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
350 :     x = if(uni) x[FALSE] else x)
351 : maechler 1109 })
352 :    
353 :     ## ``generic'' coercion to diagonalMatrix : build on isDiagonal() and diag()
354 :     setAs("Matrix", "diagonalMatrix",
355 :     function(from) {
356 : mmaechler 2341 d <- dim(from)
357 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
358 : mmaechler 2341 if(!isDiagonal(from)) stop("matrix is not diagonal")
359 :     ## else:
360 :     x <- diag(from)
361 :     if(is.logical(x)) {
362 :     cl <- "ldiMatrix"
363 :     uni <- allTrue(x)
364 :     } else {
365 :     cl <- "ddiMatrix"
366 :     uni <- allTrue(x == 1)
367 :     storage.mode(x) <- "double"
368 :     } ## TODO: complex
369 :     new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
370 :     x = if(uni) x[FALSE] else x)
371 : maechler 1109 })
372 :    
373 : maechler 1708
374 : mmaechler 2185 setMethod("diag", signature(x = "diagonalMatrix"),
375 :     function(x = 1, nrow, ncol) .diag.x(x))
376 : maechler 1708
377 : maechler 2098 subDiag <- function(x, i, j, ..., drop) {
378 : mmaechler 2508 x <- as(x, "CsparseMatrix") ## << was "TsparseMatrix" (Csparse is faster now)
379 : maechler 1799 x <- if(missing(i))
380 :     x[, j, drop=drop]
381 :     else if(missing(j))
382 : mmaechler 2363 if(nargs() == 4) x[i, , drop=drop] else x[i, drop=drop]
383 : maechler 1799 else
384 :     x[i,j, drop=drop]
385 : maechler 2120 if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
386 : maechler 1799 }
387 :    
388 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
389 :     j = "index", drop = "logical"), subDiag)
390 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
391 : mmaechler 2363 j = "missing", drop = "logical"),
392 :     function(x, i, j, ..., drop) {
393 :     na <- nargs()
394 :     Matrix.msg("diag[i,m,l] : nargs()=", na, .M.level = 2)
395 :     if(na == 4)
396 :     subDiag(x, i=i, , drop=drop)
397 :     else subDiag(x, i=i, drop=drop)
398 :     })
399 : maechler 1799 setMethod("[", signature(x = "diagonalMatrix", i = "missing",
400 :     j = "index", drop = "logical"),
401 : maechler 2098 function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
402 : maechler 1799
403 : maechler 1617 ## When you assign to a diagonalMatrix, the result should be
404 : maechler 1708 ## diagonal or sparse ---
405 :     ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
406 : maechler 2098 ## Only(?) current bug: x[i] <- value is wrong when i is *vector*
407 :     replDiag <- function(x, i, j, ..., value) {
408 : mmaechler 2811 x <- as(x, "CsparseMatrix")# was "Tsparse.." till 2012-07
409 : maechler 1710 if(missing(i))
410 :     x[, j] <- value
411 : maechler 2098 else if(missing(j)) { ## x[i , ] <- v *OR* x[i] <- v
412 :     na <- nargs()
413 :     ## message("diagnosing replDiag() -- nargs()= ", na)
414 :     if(na == 4)
415 :     x[i, ] <- value
416 :     else if(na == 3)
417 :     x[i] <- value
418 :     else stop("Internal bug: nargs()=",na,"; please report")
419 :     } else
420 : maechler 1710 x[i,j] <- value
421 :     if(isDiagonal(x)) as(x, "diagonalMatrix") else x
422 :     }
423 : maechler 1617
424 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
425 :     j = "index", value = "replValue"), replDiag)
426 : maechler 2098
427 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
428 :     j = "missing", value = "replValue"),
429 : maechler 2098 function(x,i,j, ..., value) {
430 :     ## message("before replDiag() -- nargs()= ", nargs())
431 :     if(nargs() == 3)
432 :     replDiag(x, i=i, value=value)
433 :     else ## nargs() == 4 :
434 :     replDiag(x, i=i, , value=value)
435 :     })
436 :    
437 : mmaechler 2192 setReplaceMethod("[", signature(x = "diagonalMatrix",
438 :     i = "matrix", # 2-col.matrix
439 : maechler 2096 j = "missing", value = "replValue"),
440 : maechler 2098 function(x,i,j, ..., value) {
441 : maechler 2096 if(ncol(i) == 2) {
442 :     if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
443 : mmaechler 2192 if(x@diag == "U") {
444 :     one <- as1(x@x)
445 :     if(any(value != one | is.na(value))) {
446 :     x@diag <- "N"
447 :     x@x <- rep.int(one, x@Dim[1])
448 : mmaechler 2811 } else return(x)
449 : mmaechler 2192 }
450 : maechler 2096 x@x[ii] <- value
451 :     x
452 :     } else { ## no longer diagonal, but remain sparse:
453 : mmaechler 2239 x <- as(x, "TsparseMatrix")
454 : maechler 2096 x[i] <- value
455 :     x
456 :     }
457 :     }
458 :     else { # behave as "base R": use as if vector
459 :     x <- as(x, "matrix")
460 :     x[i] <- value
461 :     Matrix(x)
462 :     }
463 :     })
464 :    
465 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
466 :     j = "index", value = "replValue"),
467 : maechler 2098 function(x,i,j, ..., value) replDiag(x, j=j, value=value))
468 : maechler 1710
469 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
470 : mmaechler 2239 value = "sparseMatrix"),
471 : mmaechler 2207 function (x, i, j, ..., value)
472 :     callGeneric(x=x, , j=j, value = as(value, "sparseVector")))
473 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
474 : mmaechler 2239 value = "sparseMatrix"),
475 : mmaechler 2207 function (x, i, j, ..., value)
476 :     callGeneric(x=x, i=i, , value = as(value, "sparseVector")))
477 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
478 : mmaechler 2239 value = "sparseMatrix"),
479 : mmaechler 2207 function (x, i, j, ..., value)
480 :     callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))
481 : maechler 1710
482 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
483 :     value = "sparseVector"),
484 :     replDiag)
485 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
486 :     value = "sparseVector"),
487 :     replDiag)
488 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
489 :     value = "sparseVector"),
490 :     replDiag)
491 :    
492 :    
493 : maechler 1109 setMethod("t", signature(x = "diagonalMatrix"),
494 :     function(x) { x@Dimnames <- x@Dimnames[2:1] ; x })
495 :    
496 : maechler 1331 setMethod("isDiagonal", signature(object = "diagonalMatrix"),
497 :     function(object) TRUE)
498 :     setMethod("isTriangular", signature(object = "diagonalMatrix"),
499 :     function(object) TRUE)
500 : maechler 1109 setMethod("isSymmetric", signature(object = "diagonalMatrix"),
501 : maechler 2112 function(object, ...) TRUE)
502 : maechler 1109
503 : maechler 2112 setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
504 :     setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)
505 :    
506 : maechler 2133 setMethod("chol", signature(x = "ddiMatrix"),
507 :     function(x, pivot, ...) {
508 : mmaechler 2183 if(x@diag == "U") return(x)
509 :     ## else
510 : maechler 2133 if(any(x@x < 0))
511 :     stop("chol() is undefined for diagonal matrix with negative entries")
512 : maechler 1654 x@x <- sqrt(x@x)
513 :     x
514 :     })
515 :     ## chol(L) is L for logical diagonal:
516 : maechler 2133 setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
517 : maechler 1654
518 : mmaechler 2175 setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
519 : mmaechler 2185 function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
520 : mmaechler 2175
521 : mmaechler 2183 setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
522 :     function(x, type, ...) {
523 :     if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix"
524 :     type <- toupper(substr(type[1], 1, 1))
525 :     isU <- (x@diag == "U") # unit-diagonal
526 :     if(type == "F") sqrt(if(isU) n else sum(x@x^2))
527 :     else { ## norm == "I","1","O","M" :
528 :     if(isU) 1 else max(abs(x@x))
529 :     }
530 :     })
531 :    
532 :    
533 :    
534 : maechler 1109 ## Basic Matrix Multiplication {many more to add}
535 : maechler 1654 ## ---------------------
536 :     ## Note that "ldi" logical are treated as numeric
537 : maechler 1109 diagdiagprod <- function(x, y) {
538 : mmaechler 2633 dimCheck(x,y)
539 : maechler 1109 if(x@diag != "U") {
540 : maechler 1654 if(y@diag != "U") {
541 :     nx <- x@x * y@x
542 :     if(is.numeric(nx) && !is.numeric(x@x))
543 :     x <- as(x, "dMatrix")
544 :     x@x <- as.numeric(nx)
545 :     }
546 :     return(x)
547 : maechler 1109 } else ## x is unit diagonal
548 :     return(y)
549 :     }
550 :    
551 : maechler 1654 setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
552 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
553 :    
554 : maechler 1654 formals(diagdiagprod) <- alist(x=, y=x)
555 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
556 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
557 : maechler 1654 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
558 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
559 : maechler 1654 setMethod("crossprod", signature(x = "diagonalMatrix", y = "missing"),
560 :     diagdiagprod, valueClass = "ddiMatrix")
561 :     setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"),
562 :     diagdiagprod, valueClass = "ddiMatrix")
563 : maechler 1109
564 :    
565 :     diagmatprod <- function(x, y) {
566 : mmaechler 2183 ## x is diagonalMatrix
567 : maechler 1109 dx <- dim(x)
568 :     dy <- dim(y)
569 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
570 :     as(if(x@diag == "U") y else x@x * y, "Matrix")
571 :     }
572 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
573 : maechler 1654 diagmatprod)
574 : mmaechler 2183 ## sneaky .. :
575 : maechler 1109 formals(diagmatprod) <- alist(x=, y=NULL)
576 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),
577 : maechler 1654 diagmatprod)
578 : maechler 1109
579 : mmaechler 2183 diagGeprod <- function(x, y) {
580 : maechler 1109 dx <- dim(x)
581 :     dy <- dim(y)
582 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
583 :     if(x@diag != "U")
584 :     y@x <- x@x * y@x
585 :     y
586 :     }
587 : mmaechler 2183 setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
588 :     setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
589 :     formals(diagGeprod) <- alist(x=, y=NULL)
590 : maechler 1109 setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
591 : mmaechler 2183 diagGeprod, valueClass = "dgeMatrix")
592 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"),
593 :     diagGeprod)
594 : maechler 1109
595 : mmaechler 2183 matdiagprod <- function(x, y) {
596 :     dx <- dim(x)
597 :     dy <- dim(y)
598 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
599 :     Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1]))
600 :     }
601 : maechler 1109 setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
602 : mmaechler 2183 matdiagprod)
603 :     formals(matdiagprod) <- alist(x=, y=NULL)
604 :     setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"),
605 :     matdiagprod)
606 : maechler 1109
607 : mmaechler 2183 gediagprod <- function(x, y) {
608 :     dx <- dim(x)
609 :     dy <- dim(y)
610 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
611 :     if(y@diag == "N")
612 :     x@x <- x@x * rep(y@x, each = dx[1])
613 :     x
614 :     }
615 :     setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod)
616 :     setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod)
617 :     formals(gediagprod) <- alist(x=, y=NULL)
618 :     setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"),
619 :     gediagprod)
620 :     setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"),
621 :     gediagprod)
622 : maechler 1109
623 : maechler 1295 ## crossprod {more of these}
624 : maechler 1109
625 : maechler 1295 ## tcrossprod --- all are not yet there: do the dense ones here:
626 : maechler 1109
627 : mmaechler 2183 setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
628 :     function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix"))
629 :     setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
630 :     function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y)
631 :    
632 :    
633 : maechler 1295 ## FIXME:
634 :     ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
635 :     ## function(x, y = NULL) {
636 :     ## })
637 : maechler 1109
638 : dmbates 2417 Cspdiagprod <- function(x, y) {
639 : dmbates 2458 dx <- dim(x <- .Call(Csparse_diagU2N, x))
640 : dmbates 2417 dy <- dim(y)
641 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
642 : mmaechler 2674 if(y@diag == "N") {
643 :     if(!all(y@x[1L] == y@x[-1L]) && is(x, "symmetricMatrix"))
644 :     x <- as(x, "generalMatrix")
645 :     ind <- rep.int(seq_len(dx[2]), x@p[-1] - x@p[-dx[2]-1L])
646 :     x@x <- x@x * y@x[ind]
647 :     }
648 : mmaechler 2608 if(is(x, "compMatrix") && length(xf <- x@factors)) {
649 :     ## instead of dropping all factors, be smart about some
650 :     ## TODO ......
651 :     x@factors <- list()
652 :     }
653 : dmbates 2417 x
654 :     }
655 : maechler 1109
656 : dmbates 2417 diagCspprod <- function(x, y) {
657 :     dx <- dim(x)
658 : dmbates 2458 dy <- dim(y <- .Call(Csparse_diagU2N, y))
659 : dmbates 2417 if(dx[2] != dy[1]) stop("non-matching dimensions")
660 : mmaechler 2674 if(x@diag == "N") {
661 :     if(!all(x@x[1L] == x@x[-1L]) && is(y, "symmetricMatrix"))
662 :     y <- as(y, "generalMatrix")
663 :     y@x <- y@x * x@x[y@i + 1L]
664 :     }
665 : mmaechler 2608 if(is(y, "compMatrix") && length(yf <- y@factors)) {
666 :     ## instead of dropping all factors, be smart about some
667 :     ## TODO
668 :     keep <- character()
669 :     if(iLU <- names(yf) == "LU") {
670 :     ## TODO keep <- "LU"
671 :     }
672 :     y@factors <- yf[keep]
673 :     }
674 : dmbates 2417 y
675 :     }
676 :    
677 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
678 :     function(x, y = NULL) diagCspprod(x, y))
679 :    
680 : maechler 1799 setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
681 : dmbates 2417 function(x, y = NULL) diagCspprod(x, as(y, "CsparseMatrix")))
682 : maechler 1295
683 : dmbates 2417 ## Prefer calling diagCspprod to Cspdiagprod if going to transpose anyway
684 :     ## x'y == (y'x)'
685 :     setMethod("crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
686 :     function(x, y = NULL) t(diagCspprod(y, x)))
687 :    
688 : maechler 1799 setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
689 : dmbates 2417 function(x, y = NULL) t(diagCspprod(y, as(x, "Csparsematrix"))))
690 : maechler 1799
691 : dmbates 2417 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
692 :     function(x, y = NULL) diagCspprod(x, t(y)))
693 :    
694 : maechler 1799 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
695 : dmbates 2417 function(x, y = NULL) diagCspprod(x, t(as(y, "CsparseMatrix"))))
696 : maechler 1799
697 : dmbates 2417 setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
698 :     function(x, y = NULL) Cspdiagprod(x, y))
699 :    
700 : maechler 1799 setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
701 : dmbates 2417 function(x, y = NULL) Cspdiagprod(as(x, "CsparseMatrix"), y))
702 : mmaechler 2472
703 : dmbates 2417 setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
704 :     function(x, y) diagCspprod(x, y))
705 : maechler 1799
706 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
707 : dmbates 2417 function(x, y) diagCspprod(as(x, "CsparseMatrix"), y))
708 : mmaechler 2472
709 : mmaechler 2183 setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
710 : dmbates 2417 function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y))
711 :    
712 : maechler 1799 setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
713 : dmbates 2417 function(x, y) Cspdiagprod(x, y))
714 :    
715 : maechler 1799 ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
716 :     ## do indeed work by going through sparse (and *not* ddense)!
717 :    
718 :     setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
719 :     function(a, b, ...) {
720 :     a@x <- 1/ a@x
721 :     a@Dimnames <- a@Dimnames[2:1]
722 :     a
723 :     })
724 :    
725 :     solveDiag <- function(a, b, ...) {
726 : mmaechler 2633 if(a@Dim[1] != nrow(b))
727 : maechler 1799 stop("incompatible matrix dimensions")
728 :     ## trivially invert a 'in place' and multiply:
729 :     a@x <- 1/ a@x
730 :     a@Dimnames <- a@Dimnames[2:1]
731 :     a %*% b
732 :     }
733 :     setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"),
734 :     solveDiag)
735 :     setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
736 :     solveDiag)
737 :    
738 : maechler 2106 ## Schur() ---> ./eigen.R
739 : maechler 1799
740 :    
741 :    
742 : mmaechler 2175 ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
743 : maechler 1295
744 : maechler 1655 ## Use function for several signatures, in order to evade
745 : mmaechler 2175 diagOdiag <- function(e1,e2) {
746 :     ## result should also be diagonal _ if possible _
747 : maechler 1655 r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
748 : mmaechler 2175 ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
749 :     r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
750 :     if(is.numeric(e2@x)) 0 else FALSE)
751 :     if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* diagonal
752 : mmaechler 2814 if(is.numeric(r)) { # "double" *or* "integer"
753 : mmaechler 2175 if(is.numeric(e2@x)) {
754 :     e2@x <- r; return(.diag.2N(e2)) }
755 :     if(!is.numeric(e1@x))
756 :     ## e.g. e1, e2 are logical;
757 :     e1 <- as(e1, "dMatrix")
758 : mmaechler 2814 if(!is.double(r)) r <- as.double(r)
759 : mmaechler 2175 }
760 :     else if(is.logical(r))
761 :     e1 <- as(e1, "lMatrix")
762 :     else stop("intermediate 'r' is of type", typeof(r))
763 :     e1@x <- r
764 :     .diag.2N(e1)
765 : maechler 1655 }
766 : mmaechler 2175 else { ## result not diagonal, but at least symmetric:
767 : mmaechler 2496 ## e.g., m == m
768 : mmaechler 2175 isNum <- (is.numeric(r) || is.numeric(r00))
769 :     isLog <- (is.logical(r) || is.logical(r00))
770 : mmaechler 2496 Matrix.msg("exploding <diag> o <diag> into dense matrix", .M.level = 2)
771 : mmaechler 2175 d <- e1@Dim
772 :     n <- d[1]
773 :     stopifnot(length(r) == n)
774 : mmaechler 2814 if(isNum && !is.double(r)) r <- as.double(r)
775 : mmaechler 2175 xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
776 :     newcl <-
777 : mmaechler 2811 paste0(if(isNum) "d" else if(isLog) {
778 : mmaechler 2175 if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l"
779 : mmaechler 2811 } else stop("not yet implemented .. please report"), "syMatrix")
780 : mmaechler 2175
781 :     new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
782 :     }
783 : maechler 1655 }
784 :    
785 : mmaechler 2175 ### This would be *the* way, but we get tons of "ambiguous method dispatch"
786 : mmaechler 2185 ## we use this hack instead of signature x = "diagonalMatrix" :
787 :     diCls <- names(getClass("diagonalMatrix")@subclasses)
788 : mmaechler 2175 if(FALSE) {
789 : maechler 1655 setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
790 :     diagOdiag)
791 : mmaechler 2175 } else { ## These are just for method disambiguation:
792 :     for(c1 in diCls)
793 :     for(c2 in diCls)
794 :     setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
795 :     }
796 : maechler 1655
797 : mmaechler 2493 ## diagonal o triangular |--> triangular
798 :     ## diagonal o symmetric |--> symmetric
799 : maechler 1845 ## {also when other is sparse: do these "here" --
800 :     ## before conversion to sparse, since that loses "diagonality"}
801 : mmaechler 2811 diagOtri <- function(e1,e2) {
802 :     ## result must be triangular
803 :     r <- callGeneric(d1 <- .diag.x(e1), diag(e2)) # error if not "compatible"
804 :     ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
805 :     e1.0 <- if(.n1 <- is.numeric(d1 )) 0 else FALSE
806 :     r00 <- callGeneric(e1.0, if(.n2 <- is.numeric(e2[0])) 0 else FALSE)
807 :     if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* triangular
808 :     diag(e2) <- r
809 :     ## check what happens "in the triangle"
810 :     e2.2 <- if(.n2) 2 else TRUE
811 :     if(!callGeneric(e1.0, e2.2) == e2.2) { # values "in triangle" can change:
812 :     n <- dim(e2)[1L]
813 :     it <- indTri(n, upper = (e2@uplo == "U"))
814 :     e2[it] <- callGeneric(e1.0, e2[it])
815 :     }
816 :     e2
817 :     }
818 :     else { ## result not triangular ---> general
819 :     rr <- as(e2, "generalMatrix")
820 :     diag(rr) <- r
821 :     rr
822 :     }
823 :     }
824 : maechler 1845
825 : mmaechler 2811
826 :     setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "triangularMatrix"),
827 :     diagOtri)
828 :     ## For the reverse, Ops == "Arith" | "Compare" | "Logic"
829 :     ## 'Arith' := '"+"', '"-"', '"*"', '"^"', '"%%"', '"%/%"', '"/"'
830 :     setMethod("Arith", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
831 :     function(e1,e2)
832 :     { ## this must only trigger for *dense* e1
833 :     switch(.Generic,
834 :     "+" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), .diag.x(e2)),
835 :     "-" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), - .diag.x(e2)),
836 :     "*" = {
837 :     n <- e2@Dim[1L]
838 :     d2 <- if(e2@diag == "U") { # unit-diagonal
839 :     d <- rep.int(as1(e2@x), n)
840 :     e2@x <- d
841 :     e2@diag <- "N"
842 :     d
843 :     } else e2@x
844 :     e2@x <- diag(e1) * d2
845 :     e2
846 :     },
847 :     "^" = { ## will be dense ( as <ANY> ^ 0 == 1 ):
848 :     e1 ^ as(e2, "denseMatrix")
849 :     },
850 :     ## otherwise:
851 :     callGeneric(e1, diag2Tsmart(e2,e1)))
852 :     })
853 :    
854 :     ## Compare --> 'swap' (e.g. e1 < e2 <==> e2 > e1 ):
855 :     setMethod("Compare", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
856 :     .Cmp.swap)
857 :     ## '&' and "|' are commutative:
858 :     setMethod("Logic", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
859 :     function(e1,e2) callGeneric(e2, e1))
860 :    
861 : maechler 1655 ## For almost everything else, diag* shall be treated "as sparse" :
862 : maechler 1295 ## These are cheap implementations via coercion
863 :    
864 : maechler 2144 ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
865 :     ## and because we can save an .M.kind() call, we use this explicit
866 :     ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
867 :     ##
868 :     ## ddi*:
869 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
870 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
871 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
872 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
873 : maechler 2144 ## ldi*
874 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
875 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
876 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
877 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
878 : maechler 1654
879 : mmaechler 2820 ## Ops: Arith --> numeric : "dMatrix"
880 :     ## Compare --> logical
881 :     ## Logic --> logical: "lMatrix"
882 : mmaechler 2175
883 : mmaechler 2820 ## Other = "numeric" : stay diagonal if possible
884 : mmaechler 2175 ## ddi*: Arith: result numeric, potentially ddiMatrix
885 : mmaechler 2813 for(arg2 in c("numeric","logical"))
886 :     setMethod("Arith", signature(e1 = "ddiMatrix", e2 = arg2),
887 : maechler 2144 function(e1,e2) {
888 : mmaechler 2820 n <- e1@Dim[1]
889 : maechler 2144 f0 <- callGeneric(0, e2)
890 :     if(all(is0(f0))) { # remain diagonal
891 : maechler 2157 L1 <- (le <- length(e2)) == 1L
892 : mmaechler 2820 if(e1@diag == "U") {
893 :     if(any((r <- callGeneric(1, e2)) != 1)) {
894 :     e1@diag <- "N"
895 :     e1@x[seq_len(n)] <- r # possibly recycling r
896 :     } ## else: result = e1 (is "U" diag)
897 :     } else {
898 : maechler 2144 r <- callGeneric(e1@x, e2)
899 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
900 :     e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
901 :     }
902 :     e1
903 :     } else
904 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
905 : maechler 2144 })
906 : maechler 1655
907 : mmaechler 2813 for(arg1 in c("numeric","logical"))
908 :     setMethod("Arith", signature(e1 = arg1, e2 = "ddiMatrix"),
909 : maechler 2144 function(e1,e2) {
910 : mmaechler 2820 n <- e2@Dim[1]
911 : maechler 2144 f0 <- callGeneric(e1, 0)
912 :     if(all(is0(f0))) { # remain diagonal
913 : maechler 2157 L1 <- (le <- length(e1)) == 1L
914 : mmaechler 2820 if(e2@diag == "U") {
915 :     if(any((r <- callGeneric(e1, 1)) != 1)) {
916 :     e2@diag <- "N"
917 :     e2@x[seq_len(n)] <- r # possibly recycling r
918 :     } ## else: result = e2 (is "U" diag)
919 :     } else {
920 : maechler 2144 r <- callGeneric(e1, e2@x)
921 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
922 :     e2@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
923 :     }
924 :     e2
925 :     } else
926 :     callGeneric(e1, diag2tT.u(e2,e1, "d"))
927 : maechler 2144 })
928 : mmaechler 2175
929 :     ## ldi* Arith --> result numeric, potentially ddiMatrix
930 : mmaechler 2813 for(arg2 in c("numeric","logical"))
931 :     setMethod("Arith", signature(e1 = "ldiMatrix", e2 = arg2),
932 : mmaechler 2175 function(e1,e2) {
933 : mmaechler 2820 n <- e1@Dim[1]
934 : mmaechler 2175 f0 <- callGeneric(0, e2)
935 :     if(all(is0(f0))) { # remain diagonal
936 :     L1 <- (le <- length(e2)) == 1L
937 : mmaechler 2820 E <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE
938 :     ## E <- copyClass(e1, "ddiMatrix", check=FALSE)
939 :     ## storage.mode(E@x) <- "double"
940 :     if(e1@diag == "U") {
941 :     if(any((r <- callGeneric(1, e2)) != 1)) {
942 :     E@diag <- "N"
943 :     E@x[seq_len(n)] <- r # possibly recycling r
944 :     } ## else: result = E (is "U" diag)
945 :     } else {
946 : mmaechler 2175 r <- callGeneric(e1@x, e2)
947 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
948 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
949 : mmaechler 2814 }
950 : mmaechler 2820 E
951 :     } else
952 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
953 : mmaechler 2175 })
954 :    
955 : mmaechler 2813 for(arg1 in c("numeric","logical"))
956 :     setMethod("Arith", signature(e1 = arg1, e2 = "ldiMatrix"),
957 : mmaechler 2175 function(e1,e2) {
958 : mmaechler 2820 n <- e2@Dim[1]
959 : mmaechler 2175 f0 <- callGeneric(e1, 0)
960 :     if(all(is0(f0))) { # remain diagonal
961 :     L1 <- (le <- length(e1)) == 1L
962 : mmaechler 2820 E <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE
963 :     ## E <- copyClass(e2, "ddiMatrix", check=FALSE)
964 :     ## storage.mode(E@x) <- "double"
965 :     if(e2@diag == "U") {
966 :     if(any((r <- callGeneric(e1, 1)) != 1)) {
967 :     E@diag <- "N"
968 :     E@x[seq_len(n)] <- r # possibly recycling r
969 :     } ## else: result = E (is "U" diag)
970 :     } else {
971 : mmaechler 2175 r <- callGeneric(e1, e2@x)
972 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
973 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
974 : mmaechler 2814 }
975 : mmaechler 2820 E
976 :     } else
977 :     callGeneric(e1, diag2tT.u(e2,e1, "l"))
978 : mmaechler 2175 })
979 :    
980 : mmaechler 2820 ## ddi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
981 :     ##
982 :     ## Note that ("numeric", "ddiMatrix") is simply swapped, e.g.,
983 :     if(FALSE) {
984 :     selectMethod("<", c("numeric","lMatrix"))# Compare
985 :     selectMethod("&", c("numeric","lMatrix"))# Logic
986 :     } ## so we don't need to define a method here :
987 :    
988 : mmaechler 2813 for(arg2 in c("numeric","logical"))
989 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = arg2),
990 : mmaechler 2175 function(e1,e2) {
991 : mmaechler 2820 n <- e1@Dim[1]
992 : mmaechler 2175 f0 <- callGeneric(0, e2)
993 :     if(all(is0(f0))) { # remain diagonal
994 :     L1 <- (le <- length(e2)) == 1L
995 : mmaechler 2820 E <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE
996 :     ## E <- copyClass(e1, "ldiMatrix", check=FALSE)
997 :     ## storage.mode(E@x) <- "logical"
998 :     if(e1@diag == "U") {
999 :     if(any((r <- callGeneric(1, e2)) != 1)) {
1000 :     E@diag <- "N"
1001 :     E@x[seq_len(n)] <- r # possibly recycling r
1002 :     } ## else: result = E (is "U" diag)
1003 :     } else {
1004 : mmaechler 2175 r <- callGeneric(e1@x, e2)
1005 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1006 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1007 : mmaechler 2814 }
1008 : mmaechler 2820 E
1009 :     } else
1010 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
1011 : mmaechler 2175 })
1012 :    
1013 : mmaechler 2820 ## ldi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
1014 : mmaechler 2813 for(arg2 in c("numeric","logical"))
1015 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = arg2),
1016 : maechler 2144 function(e1,e2) {
1017 : mmaechler 2820 n <- e1@Dim[1]
1018 : maechler 2144 f0 <- callGeneric(FALSE, e2)
1019 :     if(all(is0(f0))) { # remain diagonal
1020 : maechler 2157 L1 <- (le <- length(e2)) == 1L
1021 : mmaechler 2820
1022 :     if(e1@diag == "U") {
1023 :     if(any((r <- callGeneric(TRUE, e2)) != 1)) {
1024 :     e1@diag <- "N"
1025 :     e1@x[seq_len(n)] <- r # possibly recycling r
1026 :     } ## else: result = e1 (is "U" diag)
1027 :     } else {
1028 : maechler 2144 r <- callGeneric(e1@x, e2)
1029 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1030 :     e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1031 :     }
1032 :     e1
1033 :     } else
1034 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
1035 : maechler 2144 })
1036 : maechler 1655
1037 : maechler 2144
1038 :     ## Not {"sparseMatrix", "numeric} : {"denseMatrix", "matrix", ... }
1039 : mmaechler 2196 for(other in c("ANY", "Matrix", "dMatrix")) {
1040 :     ## ddi*:
1041 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
1042 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
1043 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
1044 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
1045 : mmaechler 2196 ## ldi*:
1046 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
1047 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
1048 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
1049 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
1050 : mmaechler 2196 }
1051 : mmaechler 2331
1052 :     ## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... :
1053 :     dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses
1054 : mmaechler 2813 names(dM.scl)[vapply(dM.scl, slot, 0, "distance") == 1] })
1055 : mmaechler 2268 for(DI in diCls) {
1056 : mmaechler 2814 dMeth <- if(extends(DI, "dMatrix"))
1057 :     function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2)
1058 :     else # "lMatrix", the only other kind for now
1059 :     function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2)
1060 : mmaechler 2331 for(c2 in c(dense.subCl, "Matrix")) {
1061 : mmaechler 2814 for(Fun in c("*", "&")) {
1062 : mmaechler 2268 setMethod(Fun, signature(e1 = DI, e2 = c2),
1063 :     function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
1064 :     setMethod(Fun, signature(e1 = c2, e2 = DI),
1065 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1066 :     }
1067 : mmaechler 2814 setMethod("^", signature(e1 = c2, e2 = DI),
1068 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1069 :     for(Fun in c("%%", "%/%", "/")) ## 0 <op> 0 |--> NaN for these.
1070 :     setMethod(Fun, signature(e1 = DI, e2 = c2), dMeth)
1071 : mmaechler 2175 }
1072 :     }
1073 : maechler 2144
1074 :    
1075 : mmaechler 2175 ### "Summary" : "max" "min" "range" "prod" "sum" "any" "all"
1076 : mmaechler 2345 ### ---------- the last 4: separately here
1077 : mmaechler 2175 for(cl in diCls) {
1078 :     setMethod("any", cl,
1079 :     function (x, ..., na.rm) {
1080 :     if(any(x@Dim == 0)) FALSE
1081 :     else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
1082 :     })
1083 : mmaechler 2341 setMethod("all", cl, function (x, ..., na.rm) {
1084 :     n <- x@Dim[1]
1085 :     if(n >= 2) FALSE
1086 :     else if(n == 0 || x@diag == "U") TRUE
1087 :     else all(x@x, ..., na.rm = na.rm)
1088 :     })
1089 :     setMethod("prod", cl, function (x, ..., na.rm) {
1090 :     n <- x@Dim[1]
1091 :     if(n >= 2) 0
1092 :     else if(n == 0 || x@diag == "U") 1
1093 :     else ## n == 1, diag = "N" :
1094 :     prod(x@x, ..., na.rm = na.rm)
1095 :     })
1096 : mmaechler 2175
1097 :     setMethod("sum", cl,
1098 :     function(x, ..., na.rm) {
1099 :     r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
1100 :     if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r
1101 :     })
1102 :     }
1103 :    
1104 :     ## The remaining ones are max, min, range :
1105 :    
1106 :     setMethod("Summary", "ddiMatrix",
1107 :     function(x, ..., na.rm) {
1108 :     if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
1109 :     else if(x@diag == "U")
1110 :     callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
1111 :     else callGeneric(x@x, 0, ..., na.rm=na.rm)
1112 :     })
1113 :     setMethod("Summary", "ldiMatrix",
1114 :     function(x, ..., na.rm) {
1115 :     if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
1116 :     else if(x@diag == "U")
1117 :     callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
1118 :     else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
1119 :     })
1120 :    
1121 :    
1122 :    
1123 : maechler 1109 ## similar to prTriang() in ./Auxiliaries.R :
1124 :     prDiag <-
1125 :     function(x, digits = getOption("digits"), justify = "none", right = TRUE)
1126 :     {
1127 :     cf <- array(".", dim = x@Dim, dimnames = x@Dimnames)
1128 :     cf[row(cf) == col(cf)] <-
1129 :     sapply(diag(x), format, digits = digits, justify = justify)
1130 :     print(cf, quote = FALSE, right = right)
1131 :     invisible(x)
1132 :     }
1133 :    
1134 : mmaechler 2237 ## somewhat consistent with "print" for sparseMatrix :
1135 :     setMethod("print", signature(x = "diagonalMatrix"), prDiag)
1136 :    
1137 : maechler 1109 setMethod("show", signature(object = "diagonalMatrix"),
1138 : maechler 1592 function(object) {
1139 :     d <- dim(object)
1140 :     cl <- class(object)
1141 : mmaechler 2203 cat(sprintf('%d x %d diagonal matrix of class "%s"',
1142 : maechler 1592 d[1], d[2], cl))
1143 : mmaechler 2203 if(d[1] < 50) {
1144 :     cat("\n")
1145 :     prDiag(object)
1146 :     } else {
1147 :     cat(", with diagonal entries\n")
1148 :     show(diag(object))
1149 :     invisible(object)
1150 :     }
1151 : maechler 1592 })
1152 : mmaechler 2813
1153 :     rm(dense.subCl, diCls)# not used elsewhere
1154 : mmaechler 2820
1155 :     setMethod("summary", signature(object = "diagonalMatrix"),
1156 :     function(object, ...) {
1157 :     d <- dim(object)
1158 :     r <- summary(object@x, ...)
1159 :     attr(r, "header") <-
1160 :     sprintf('%d x %d diagonal Matrix of class "%s"',
1161 :     d[1], d[2], class(object))
1162 :     ## use ole' S3 technology for such a simple case
1163 :     class(r) <- c("diagSummary", class(r))
1164 :     r
1165 :     })
1166 :    
1167 :     print.diagSummary <- function (x, ...) {
1168 :     cat(attr(x, "header"),"\n")
1169 :     class(x) <- class(x)[-1]
1170 :     print(x, ...)
1171 :     invisible(x)
1172 :     }

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